The report added that the rocket reached a height of 120 kilometres (75 miles).

In January, Iran said it had successfully brought a live monkey, which it named Pishgam (Pioneer), back to Earth from orbit.

But the experiment's success was disputed, when a different monkey was presented to the media after the landing.

An earlier attempt had failed in September 2011.

Iran's space programme has prompted concern among Western governments, which fear Tehran is trying to master the technology required to deliver a nuclear warhead.

The Islamic republic insists that its nuclear programme is entirely peaceful.

"By the grace of God and through the efforts of Iranian space scientists, the Pajohesh (research) rocket containing the second live space monkey, named Fargam (Auspicious), was sent into space and brought back to Earth safely," Rouhani said in his message.

State television broadcast footage of the rocket launch which state television said took place on Saturday morning.

A helicopter brought a capsule to the scene which the reporter said contained the monkey, and later footage of a monkey wearing a red shirt was shown.

Iran's space programme was heavily promoted by Rouhani's controversial predecessor Mahmoud Ahmadinejad, who quipped in February that he was "ready to be the first Iranian to be sacrificed by the scientists of my country and go into space, even though I know there are a lot of candidates".

To the dismay of animal welfare groups, Fargam was following in the footsteps of a menagerie of dogs and monkeys that were among the early stars of the US and Soviet space programmes in the 1960s.

Earlier this year, Iranian space officials raised the prospect of sending a Persian cat into space.

"Iran's archaic experiment... is a throwback to the primitive techniques of the 1950s," People for the Ethical Treatment of Animals spokesman Ben Williamson said at the time.

The stated aim of Iran's programme is a manned launch by 2020.

The programme deeply unsettles Western governments as the technology used in space rockets can also be used in ballistic missiles.

The UN Security Council has imposed an almost total embargo on the export of nuclear and space technology to Iran since 2007.

Tehran denies its space programme has any link with its alleged nuclear ambitions.